Unit 8: Analytic Geometry (standards and definitions/postulates/theorems)
Wednesday, May 15th, 2013
Today was the test day!
IW:
Please go back through the test (blank copy here) and re-do any problems that you got stuck on with the help of a friend, the internet, your text, Mr. O'Brien, etc. Please also re-do any ThatQuiz questions that you didn't get 100% on (they won't save until you get 100%!).
Monday, May 13th, 2013
Today was our test revision day. We began by becoming "proficient" (i.e. the star is filled in!) in these Khan Academy exercises:
Make sure you are proficient in each Khan Academy category above.
p. 479/1-11, 13-20
Organize IW #1-#5, making sure each is checked and corrected (showing working!). Staple cover page on the packet.
Thursday, May 9th, 2013
We began class by doing the ThatQuiz warm-up. We corrected the quiz and went over the IW. We revised the Point-Slope form of a line and then worked on problems.
IW #4:
p. 474/7, 9, 15, 17, 19, 21, 23, 25, 27, 35, 39
Tuesday, May 7th, 2013
We began class by going over IW questions and then used Example 1 on p. 463 to discuss how to prove theorems analytically. The steps:
Determine the hypothesis and the conclusion.
Use the hypothesis to draw and label a figure (See Tables 9.1 & 9.2 on p. 462.
Make a plan for how to work from the hypothesis to the conclusion.
Write the proof, being sure to order statements correctly and justify each statement.
IW #3:
Read Examples 2, 3, & 4 on p. 464-466
p. 466/1, 3, 4, 7, 10, 11, 12
Wednesday, May 1st, 2013
We began with another coordinate geometry warm-up on ThatQuiz, all aiming for 90% or better. We discussed the IW. We then did some internet research in small groups and shared our findings: the *why* the distance formula, midpoint formula, and perpendicular line slope relationship.
IW #2:
Bring your laptops for NWEA's on Friday...
p. 441/11, 17, 25, 27, 29, 31, 33, 37, 39
p. 451/35, 37
p. 459/25, 27, 31, 35
Quiz on 9.1 to 9.3 on Tuesday
Monday, April 29th, 2013
We began with a coordinate geometry warm-up to determine our understanding before correcting the Unit 7 test on areas and volumes. We finished with notes on the distance formula, midpoint formula, slope formula, and parallel/perpendicular line slope relationships and did some classwork.
IW #1:
p. 441/2, 5, 7, 9, 21, 23
p. 451/1, 5, 9, 11, 13, 15, 17, 21, 25, 27, 31
p. 459/1, 3, 5, 7, 9, 11, 13, 15, 17, 23
Unit 7: Areas & Volumes (standards and definitions/postulates/theorems)
We began class with the ThatQuiz challenge question set from the last quiz. After going over IW questions, we spent the period working on surface area and volume problems (solutions here ) and IW #6 in preparation for Thursday's test.
IW #6:
p. 386/4-9, 16
p. 434/1-14
Organize IW #1-#6. Be sure you have the working for each problem (as appropriate) and check each answer in the back (or online). Correct any errors.
Friday, April 12th, 2013
We began class by correcting the IW quiz and discussing old IW questions. We then investigated polyhedra leading to Euler's Formula.
Make sure you are "proficient" at the four Khan Academy sets from Unit 7 (the two from IW #1, the one from last class, and the one from today). When you are proficient, the star is shaded in.
If you weren't in class, be sure you've done the ThatQuiz problems
We began by doing the area practice problems at the ThatQuiz link above (be sure to have scratch paper!). This led to a discussion of surface area and how to dissect a cylinder into its net. We then worked on these shaded area problems. We discussed the area formulas on p. 382 & 383, including Heron's area formula for triangles and the cool formula for the area of a triangle by its inscribed circle and perimeter... We then looked at our solids and some area and volume formulas.
IW #2:
Make sure you are "proficient" at the three Khan Academy sets from Unit 7 (the two from IW #1 and the one from today). When you are proficient, the star is shaded in.
If you weren't in class, be sure you've done the ThatQuiz problems
We began by going to the online Grade Calculator (make a copy for yourself (File- Make a copy...) and play with it). We then corrected the quiz and went over IW questions before taking a look at the final two sections of Chapter 6: locus and concurrence of lines. We reviewed the appropriate theorems and learned the mnemonic Many Cute People Believe Colorful Apples Bake In Airy Ovens. Questions on these two sections will be extra credit, but that's a great way to offset careless errors!!!
IW #8:
If you didn't finish in class, copy Section 6-5 & 6-6 theorems into your Google Docs notebooks
Practice Test: p. 333/1-16 & p. 387/10-15 (be sure to check and correct errors!!!)
We began by going over any questions before the quiz. Those who finished early copied the seven Section 6-4 theorems into your Google Docs notebooks. After we reviewed the theorems, we worked on the assigned IW problems.
IW #7:
If you didn't finish in class, copy Section 6-4 theorems into your Google Docs notebooks
p. 310/1-7 odd, 17, 19, 21, 25
If necessary, spend the remainder of your hour finishing the IW #6 packet
Due to the snow day, Tuesday's work bumped to Thursday.
Mr. O'Brien is out this week. Your sub Mr. Wheelis will help you out- he loves geometry! You may also email questions directly to Mr. O'B (link on left).
Tuesday
Begin by making sure that you've checked your Unit 6 quiz and reading notes sheet using the solutions posted with IW #5 below. Got questions on these or IW #5? Ask Mr. Wheelis...
Spend the remainder of class working on the IW #6 sheets (answers posted below). Work from the back of the packet (9-7) to the front, as you might not have time to do all the problems in the hour dedicated to IW outside of class. Some problems involve the quadratic formula.
The questions on the quiz on Thursday will be taken directly from these four pages. You will not be able to use IW #6 during Thursday’s quiz (to avoid copying of answers without understanding).
Read Section 6-3 using the reading guide sheet and check your answers here
Copy Theorems from 6.3 into your Google Docs notebook.
p. 302/1, 3, 7-23 odd
Tuesday, March 12th, 2013
We began class with the IW quiz. We then went over the most recent IW questions and learned about arc length, sectors, and circle segments.
IW #4:
Copy Theorems from 7.4 & 7.5 into your Google Docs notebook.
p. 371/9, 15, 19, 23, 27, 31, 33, 39
p. 377/1, 3, 7, 13, 17, 19, 25, 37, 39
Friday, March 8th, 2013
We began class by taking a look at the Section 6.2 theorems involving secants and tangents. We used this applet to prove some of them. This led us to discuss the IW. We ended class with π, circumference, area, arc length, and sector area.
IW #3:
p. 293/4, 8, 10, 12, 14, 16, 18, 22, 28
p. 370/1, 5, 7, 11, 21
Wednesday, March 6th, 2013
We began class by further investigating inscribed angles. Log into the Khan Academy and do this these three inscribed angle exercise sets: angle side on the diameter , angle sides enclosing the diameter , and angle sides outside the diameter. Before you do each problem set, watch the set of hints for each type; they prove that powerful Theorem 6.1.2. After our circle investigation, we corrected the Unit 5 test. We reviewed the section 6.1 theorems and went over the IW.
IW #2:
Copy Theorems 6.2.1 to 6.2.8 into your Google Docs notebook.
We began class by spending a little more time on the Unit 5 test. We then began our Unit 6 work by defining the following terms in our Google Docs notebook: circle, radius, chord, diameter, congruent circles, concentric circles, arc, semicircle, minor arc, major arc, central angle, inscribed angle, intercepted arc, measure of an arc, and congruent arcs. We then discussed a number of circle postulates and theorems and added them to our notebooks.
IW #1:
Copy Postulates 16 & 17 and Theorems 6.1.1 to 6.1.10 into your Google Docs notebook.
We began class by going over a special right triangle problem from the IW (if you are having trouble with special right triangles, this video might help!). We then investigated the neat theorem about how a triangle's angle bisector splits the side opposite it proportionally to the two sides that make it up. We proved the theorem and then took the quiz. We spent the remainder of class with this investigation:
Construct a triangle in Geogebra and a point anywhere on its interior.
Extend a ray from each vertex through the point on the interior and mark the points where the rays intersect each side.
Starting at one vertex, label the six segments that the triangle sides are divided into with the names a, b, c, d, e, and f. Find the ratio of a/b, c/d, and e/f and then multiply these ratios together. Surprised?!?
Email your file to me.
Write a paragraph proof of this amazing result (see p. 262 for guidance).
IW #7:
Finish the investigation from class if necessary and then copy Theorem 5.6.4 into your Google Docs notebook.
Make sure IW #1 to #6 are finished, checked, and corrected.
We began class by doing some classwork practice: p. 249/26-29, 33, 38. We then corrected the quiz and spent some time discussing the two special right triangles and the IW. We finished by looking at dividing segments proportionally.
IW #6:
p. 263/2-16 even, 23
Copy Theorems 5.6.1 to 5.6.3 into your Google Docs notebook (use link above if you'd like)
Quiz on the special right triangles- closed notes! Memorize the relationships...
Monday, February 11th, 2013
We began class with the quiz. Following that, we went over IW questions and learned about Pythagorean triples and the power of similarity for triangle problems. We finished by looking at our two special triangles: the 30-60-90, and the 45-45-90.
IW #5:
Use the internet to find a cool formula to generate some Pythagorean Triples. Email it to me at bill_obrien@fivetowns.net with: the formula, an example using the formula, a reason why you chose it over the other possible formulas out there.
Finish class sheet if necessary
p. 254/1-18 all
Copy Section 5.5 Theorems into your Google Docs notebook (use link above if you'd like)
Thursday, February 7th, 2013
We began class with notes on the geometric mean. We then constructed right triangles and their altitude inside the triangle. We printed them out and used them to discuss the geometric mean geometrically and several theorems leading to a proof of the Theorem of Pythagoras.
IW #4:
Copy Section 5.4 Theorems into your Google Docs notebook (use link above if you'd like)
pg. 248/2-18 even
Prepare for Section 5.1 to 5.3 quiz Monday (open notes, open IW's)
Tuesday, February 5th, 2013
Unfortunately, Mr. O'Brien is home with a sick daughter this morning. Fortunately, you are in the capable hands of Ms. Nightingale! To begin, please open this sketch (in Firefox or Safari). Do the following:
Drag point A to get your own triangle.
Write and solve two proportions in your notebook to find the lengths of a and of b.
Check your answer by dragging down the blue and the green dots!
When you finish, please check the even answers to IW #3 (and #1 and #2 if you have not yet done so). Ms. Nightingale will go over the posted questions in class. Please make sure you have submitted the IW #1 and IW #2 sheets into the wire basket to be checked.
Next, please open this sketch(in Firefox or Safari). Explore the three triangle similarity shortcuts and then copy Postulate 15 and Theorems 5.3.1 through 5.3.5 into your Google Docs and begin work on the practice sheet.
We began class with a warm up to solve three quadratics. We used the Show Steps button in wolframalpha and the drop down menu of different solution methods. This led to a discussion of various ways to solve quadratics- simple square roots, factoring, and the quadratic formula. We then discussed the IW. This led to an introduction to similar polygons using this Geogebra applet.
We finished by working on a classwork sheet.
IW #2:
p. 230/2-30 evens
Finish class sheet if necessary
Wednesday, January 30th, 2013
We began class by re-doing #18 from the test because of the typo. We then worked on correcting test errors in small groups. We took some notes on ratios, rates, and proportions, including three properties. We finished by working on a classwork sheet.
We began class with a self-correcting Always, Sometimes, Never quiz . The first three 100%'s earned extra credit! We then went over IW questions and made test revision questions in class for a class Jeopardy game. We finished with the game...
Practice with the Always, Sometimes, Never quiz...
Work on Unit 4 Challenge problems: pg 194/ (30, 36) pg 202 27, pg 209: (22, 25,36)
Tuesday, January 22nd, 2013
We began class by going over the midterm. We then did p. 209-10/26 & 29 in pairs (and submitted) and then worked on finishing the Unit 4 Challenge problems p. 209/22, 25, 36.
IW #6:
Finish IW #1 to #5- be sure each problem is checked and corrected!
Work on Unit 4 Challenge problems: pg 194/ (30, 36) pg 202 27, pg 209: (22, 25,36)
Monday, January 14th, 2013
We began class by correcting the quiz and discussing the midterm. We then went over IW #3 and worked on IW #4.
IW #5:
p. 208/11-21 all
Midterm revision: Practice test . Solutions are here. Be sure you've memorized your vocabulary and theorems!
Work on Unit 4 Challenge problems: pg 194 (30, 36) pg 202 27, pg 209: (22, 25,36)
Thursday, January 10th, 2013
We began class with the quiz. Following the quiz, we worked on part of IW#4. We then practiced with quadrilateral properties here. We finished by taking a look at the IW#3 questions. We learned about cyclic quadrilaterals and how to use the quadratic formula to find missing side lengths. We also talked a little about the midterm.
IW #4:
Finish sheet from class if necessary (and submit).
p. 201/8-30 even
Midterm revision: Practice test . Be sure you've memorized your vocabulary and theorems!
Work on Unit 4 Challenge problems: pg 194 (30, 36) pg 202 27, pg 209: (22, 25,36)
Tuesday, January 8th, 2013
We began class by submitting the IW and finishing the quadrilateral jigsaw. Each group then presented their findings, beginning with a definition of their quadrilateral (from the glossary). We copied the remainder of the Unit 4 theorems into our Google Docs notebooks and went over the IW questions in preparation for the quiz next class.
IW #3:
p. 192/2-30 even
Quiz next class! (open notes and open IW)
Begin Unit 4 Challenge problems: pg 194 (30, 36) pg 202 27, pg 209: (22, 25,36)
Thursday, January 4th, 2013
We began class by going over the answers to the Unit 3 test in preparation of the midterm. We then began a quadrilateral jigsaw .
IW #2:
Sheet on parallelograms (6-1) to be submitted next class
Finish Unit 3 Challenge problems: pg 137 #40, pg. 153 #36 and #41, pg. 167 #27 and #33 and Constructions: 1.) a 30-60-90 triangle with a hypotenuse of 2 inches. 2.) a 75° angle 3.) a regular hexagon with each side measuring 2 inches and 4.) pg 158 #23 (for the Unit 3 standards, go to the Archive)
Begin Unit 4 Challenge problems: pg 194 (30, 36) pg 202 27, pg 209: (22, 25,36)
Wednesday, January 2nd, 2013
We began class by correcting the Unit 3 test. We noted that the definition of perpendicular lines does *not* include the words "right angle" or 90°; perpendicular lines are lines that form congruent adjacent angles. We then explored parallelograms and some interesting properties using paper and Geogebra. This sketch shows the relationships we found. We ended class by looking at p. 184/17 & 18.
IW #1:
p. 184/3, 5, 7, 9, 10, 11, 13, 14, 21, 25, 29
Add Section 4.1 theorems (4.1.1 through 4.1.8) to your Google Docs notebook.
Finish Unit 3 Challenge problems: pg 137 #40, pg. 153 #36 and #41, pg. 167 #27 and #33 and Constructions: 1.) a 30-60-90 triangle with a hypotenuse of 2 inches. 2.) a 75° angle 3.) a regular hexagon with each side measuring 2 inches and 4.) pg 158 #23 (for the Unit 3 standards, go to the Archive)
Finish Unit 3 Challenge problems: pg 137 #40, pg. 153 #36 and #41, pg. 167 #27 and #33 and Constructions: 1.) a 30-60-90 triangle with a hypotenuse of 2 inches. 2.) a 75° angle 3.) a regular hexagon with each side measuring 2 inches and 4.) pg 158 #23
Tuesday, December 18th, 2012
We corrected the quiz and reviewed for Thursday's test with this Jeopardy game.
IW #9:
Review your Unit 3 vocabulary and theorems for Thursday's test.
We began by going over Section 3-3 questions. After the quiz, we did two constructions and then discussed *why* some constructions work: copying an angle, bisecting an angle, and constructing a perpendicular from a point not on a line. We then reviewed the triangle inequality lemmas and theorems.
IW #8:
Copy Lemmas and Theorems 3.5.1 – 3.5.10 into your Google Docs notebook (copy and paste from above if necessary.
p. 165/4-6, 14, 18, 24
Unit 3 Challenge Problems
Wednesday, December 12th, 2012
Unfortunately, Mr. O'B was out sick. From his sub plans:
Students should begin by doing proofs #1, #3, and #10 on p. 171 in groups of three to submit to you. When they finish, please give them the triangle inequality sheets and ask them to read Section 3-5 and then complete the two sheets.
Their independent work is to complete the triangle inequality sheets and begin the Challenge problems. Please ask them to check that they did the correct IW #6- there was an error in iCal on Monday (although the website had the correct IW).
IW #7:
Work on Unit 3 Challenge problems: pg 137 #40, pg. 153 #36 and #41, pg. 167 #27 and #33 and Constructions: 1.) a 30-60-90 triangle with a hypotenuse of 2 inches. 2.) a 75° angle 3.) a regular hexagon with each side measuring 2 inches and 4.) pg 158 #23
Monday, December 10th, 2012
We began class by correcting the quiz together and then we discussed the center of a triangle investigation.
IW #6:
p. 157/1-10, 15, 16, 32
Thursday, December 6th, 2012
We began class by going over the IW and taking any questions before the quiz. We then took the quiz. Those who finished early, worked on the isosceles triangle practice sheet. When everyone was finished, we learned how to construct an angle bisector, a median, an altitude, and a perpendicular bisector for a triangle. We then worked on the Triangle Middle Exploration .
We began class with the Isosceles Triangle Construction challenge. This led to some familiarity with Geogebra and then some vocabulary and theorems about isosceles triangles. We went over an IW proof together and finished by defining angle bisector, median, altitude, and perpendicular bisector for a triangle.
IW #4:
Enter new theorems into your Google Docs notebook (feel free to use the link above)
Do the optional practice quiz before Thursday's Section 3-1 & 3-2 quiz (quiz here and solutions here )
p. 151/2-5, 13-16, 21, 24, 29, 35
Friday, November 30th, 2012
We began class by going over the IW and some Unit 2 classwork. We then practiced with a congruent triangle problem set. We then looked at a special SSA case, the HL case, by looking at the triangle congruence applet. We then proved pp. 137/32 together and spent the remainder of our time working on congruence proofs from the IW. We finished class with by looking at CPCTC.
IW #3:
Finish congruent triangle problem set sheets
Enter HL and CPCTC into your Google Docs notebook (feel free to use the link above)
p. 143/9-16, 23, 27
Wednesday, November 28th, 2012
We began class by going over the Unit 2 tests. We discussed the connection between AAS and ASA and how they relate to AAA. We then used the the applet from last class to further explore the difference between SAS and SSA. We then proved pp. 137/32 together and spent the remainder of our time working on congruence proofs from the IW.
IW #2:
p. 134/21-27, 31, 33-36
Monday, November 26th, 2012
We began class by correcting the tests. We then explored triangle congruence tests using this applet: SSS, AAA, SSA, AAS, ASA, and SAS. Four became postulates/theorems, and two were discovered to be false...
IW #1:
p. 134/1-4, 6, 9-20
Add Section 3.1 definition of triangle congruence, three postulates, and one theorem to your Google Docs notebook.
We began class by going over IW questions. We then took the quiz. Those who finished early worked on the practice test. We finished class by going over the quiz.
Keep working on Unit 2 Challenge Problems in Google Docs notebook: p. 91/9, 33 & p. 98/32, 45 & p. 107/35, 38, 40. They are due the class after the test!
November 13, 2012
We began class with the quiz. Following the quiz, we read a little history of geometry on p. 118-119. We followed up by working on a group proof to submit: p. 91/29.
IW #7:
p. 123/1-17 odd, 19-32
Unit 2.4 quiz next class- open notes
Keep working on Unit 2 Challenge Problems in Google Docs notebook: p. 91/9, 33 & p. 98/32, 45 & p. 107/35, 38, 40
November 8, 2012
Due to the snow delay, we postponed the quiz to next class. We discussed the IW #5 and the theorems and corollaries for polygons.
IW #6:
p. 97/4, 6, 12, 14, 19, 26, 27 to submit next class
Unit 2 quiz next class- open notes
Keep working on Unit 2 Challenge Problems in Google Docs notebook: p. 91/9, 33 & p. 98/32, 45 & p. 107/35, 38, 40
November 6, 2012
We began class by going over IW and Quarter 1 assignments. We discussed grades and Challenge Problems. We then explored convex polygons: diagonals, interior angles, exterior angles.
IW #5:
p. 105-107/1-5, 8-20 even, 28, 31, 32, 40, 41
Unit 2 quiz next class- open notes
Keep working on Unit 2 Challenge Problems in Google Docs notebook: p. 91/9, 33 & p. 98/32, 45 & p. 107/35, 38, 40
Section 2.5 Theorems and Corollaries to your notebook
November 2, 2012
We began with a classwork assignment reviewing parallel and skew lines. We then took the quiz on Section 2.1. Mr. O'Brien gave some notes on triangles, including some vocabulary and a theorem with several corollaries. Mr. O'Brien then had to read the Riot Act on Challenge problems.
IW #4:
Mr. O'Brien will be finishing 1st quarter grades on Sunday. If you would like to do any further work on your Challenge Problems, please do so by noon Sunday.
Read Section 2.4 and add the Section 2.4 Theorems and Corollaries to your notebook
p. 96-97/1-3,5-15 odd, 16-24 even
Halloween, 2012
Mr. O'Brien is out today. After checking IW #2 (even answers posted above), the sub will give you a set of classwork practicing Sections 2.1 and 2.3. If you finish early, you may begin IW #3.
IW #3:
p. 91-92/1-18, 23-26
Quiz covering Section 2.1 next class. It will be open notes but closed texts- be sure you are organized and ready to go!
Thursday, October 25th, 2012
We began class by playing with this Geogebra applet and answering the questions in our notebooks. We then discussed the postulates and theorems from Section 2.1. We also took a moment to look at the history of the Parallel Postulate. We went over the IW and then explored some converses leading to more theorems on proving lines parallel. This led to a discussion of inverse and contrapositive and the method of indirect proof, including the Law of Negative Inference.
IW #2:
p. 80/25
p. 84-85/1, 2, 6, 7
Begin Unit 2 Challenge Problems in Google Docs notebook: p. 91/9, 33 & p. 98/32, 45 & p. 107/35, 38, 40
NWEA's next class- bring a charged laptop
Tuesday, October 23rd, 2012
We began class by reading section 2.1 and taking reading notes. We also worked on adding definitions, theorems, and postulates to our Google Docs. We then worked on correcting Unit 1 errors in small groups.
IW #1:
Finish reading notes packet and problems from the book (p. 78-79/2-20 evens)
We began class by going over the proof classwork that was due last week. We went over the IW and the rubrics for the Challenge problems and the unit standards. We spent the remainder of the period revising for the unit test.
Test Friday- closed notes. Be sure to memorize vocabulary, postulates, and theorems...
Organize IW's and staple (in order) to be submitted Friday.
Finish Challenge problems due on test day.
Thursday, October 11th, 2012
We warmed up with p. 57/21, 25, 27. We then went over the quiz and worked on revising for next week's unit test.
IW #14:
p. 68/1-22
Challenge problems due on test day, Wednesday, October 17th
Tuesday, October 9th, 2012
We began class with the quiz. We then went over the IW and the last theorems of Unit 1.
IW #13:
Proof practice packet
Challenge problems due on test day, Wednesday, October 17th
Wednesday, October 3rd, 2012
We began class by learning our final construction of the unit: construct line perpendicular at a specific point on the given line. We then worked on classwork problems p. 50/1, 5-9, 26 to submit. We went over the evens and any questions from IW #11 and finished by discussing how to prove theorems.
IW #12:
Copy Theorems 1.7.1 to 1.7.8 into your Google Docs notebook
p. 57/9-20
Monday, October 1st, 2012
We began with some angle and proof warm-up. We then corrected the IW and updated our Google Docs notebooks with Theorems 1.3.1 to 1.6.4 from p. A27 (proofs to come for some). We defined perpendicular lines, proved some theorems, and looked at relations and the Reflexive, Symmetric, Transitive properties for relations (i.e. congruence).
IW #11:
p. 50/2, 3, 4, 12, 20, 22
Thursday, September 27th, 2012
We began by correcting the quiz from last class (solutions here) and discussing expectations in an honors course. We then began our work with geometric proof.
IW #10:
p. 43/1-24
Tuesday, September 25th, 2012
We began class with a quiz on section 1.1 to 1.3 and constructions. We then corrected the probability quizzes and the angle measuring worksheet and went over old IW questions.
IW #9:
Work on finishing the Challenge problems
Friday, September 21st, 2012
We went over the probability quiz and reviewed angle vocabulary and problems.
IW #8:
Be sure IW#1 to #7 are checked and corrected.
Revise for Section 1.1 to 1.3 quiz next class (practice quiz here and answers here)
Have something written in your Google Docs notebook for each Challenge problem
Wednesday, September 19th, 2012
We began class with the quiz and then warmed up with some angle measuring using the ThatQuiz link above. We also did a little worksheet which led us into angle measuring. We added two new postulates and several angle definitions to our notebooks (Keynote slide to copy-paste from available here).
IW #7:
p. 36-38/2-12, 14-22, 24-26, 28, 41
Keep working on Challenge problems
Monday, September 17th, 2012
We began class by reviewing probability. We then went over Challenge problem expectations and began our work developing geometry as a mathematical system, building up from postulates and definitions.
IW #6:
p. 27-29/1-5, 8-12, 14-19, 28
Review for probability quiz next class (open notes)
Keep working on Challenge problems
Thursday, September 13th, 2012
We began class with the vocabulary quiz on Sections 1.1 and 1.2. We then went over IW #4, including the even answers (above). We finished our discussion on constructions (using both compass/straightedge and GeoGebra) and we then took notes on probability. Our objectives covered in class were 1.2, 1.3, and 1.9.
IW #5:
Review probability notes and bring any questions next class- quiz on Wednesday.
If you have not yet copied this Google Docs file and shared it with obrienbluester@gmail.com, please do so now.
Make sure that the working for at least one challenge problem is posted in your Google Docs notebook.
Using p. 21-27, add the 7 postulates and 7 definitions contained within the blue boxes to your Google Docs notebook.
Tuesday, September 11th, 2012
We began class by completing this introductory survey and reviewing the vocabulary of Section 1.2 with a worksheet. We discussed the Venn Diagram activity and IW #3. We learned how to make geometric constructions with a compass and straightedge and the corresponding GeoGebra tools. Our work covered objectives 1.1, 1.5, 1.9.
IW #4:
p. 19/35-47
Vocab quiz on 1.1 and 1.2 (check our Key Concepts boxes and bolded words...)
Use the internet to define the following terms from probability: conditional, independent, dependent.
Keep working on challenge problems...
Friday, September 7th, 2012
We began class by going over the IW (see even answers above). We reiterated the four elements of each IW (name, date, assignments, number) and discussed any questions, including the vocabulary words conjunction and disjunction. We reviewed the rubrics for objectives 1.1, 1.4, and 1.6 and then worked on the Venn Diagram activity. We finished with some notes on Section 1.2.
IW #3:
Read p. 10-17
p. 17/1-11, 27
Keep working on challenge problems...
Wednesday, September 5th, 2012
We began class with vanity plate introductions and discussed our use of rubrics this year. We then discussed independent work expectations, the responsibility points rubric and the independent work rubric (using this Prezi ). We began our Unit 1 work by reviewing the standards (rubrics here), the assessments, and the challenge problems. Those with laptops copied this Google Docs file and shared it with obrienbluester@gmail.com to start their class notebooks. We then took notes on sets, Venn Diagrams (using this Geogebra sketch ) and the Law of Detachment. The standards covered were 1.1, 1.4, and 1.6.
IW #2:
p. 8/2-12 even, 33, 34, 38, 41, 44
Begin work on a challenge problem
Friday, August 31st, 2012
We began class with some introductions and a discussion of the course methodology, including expectations for class, the importance of independent work, how to get help, and more. We then used some intuition, inductive and deductive reasoning to answer some interesting questions and took a brief look at the standards for the unit and the challenge problems. We finished
by reviewing rubrics using vanity name plates.
Table of Contents
Unit 8: Analytic Geometry (standards and definitions/postulates/theorems)
Wednesday, May 15th, 2013
Today was the test day!IW:
Monday, May 13th, 2013
Today was our test revision day. We began by becoming "proficient" (i.e. the star is filled in!) in these Khan Academy exercises:We also discussed old IW questions.
IW #5:
Thursday, May 9th, 2013
We began class by doing the ThatQuiz warm-up. We corrected the quiz and went over the IW. We revised the Point-Slope form of a line and then worked on problems.IW #4:
Tuesday, May 7th, 2013
We began class by going over IW questions and then used Example 1 on p. 463 to discuss how to prove theorems analytically. The steps:IW #3:
Wednesday, May 1st, 2013
We began with another coordinate geometry warm-up on ThatQuiz, all aiming for 90% or better. We discussed the IW. We then did some internet research in small groups and shared our findings: the *why* the distance formula, midpoint formula, and perpendicular line slope relationship.IW #2:
Monday, April 29th, 2013
We began with a coordinate geometry warm-up to determine our understanding before correcting the Unit 7 test on areas and volumes. We finished with notes on the distance formula, midpoint formula, slope formula, and parallel/perpendicular line slope relationships and did some classwork.IW #1:
Unit 7: Areas & Volumes (standards and definitions/postulates/theorems)
Thursday, April 25th, 2013
Test Day.IW:
Tuesday, April 23rd, 2013
We began class with the ThatQuiz challenge question set from the last quiz. After going over IW questions, we spent the period working on surface area and volume problems (solutions here ) and IW #6 in preparation for Thursday's test.IW #6:
Friday, April 12th, 2013
We began class by correcting the IW quiz and discussing old IW questions. We then investigated polyhedra leading to Euler's Formula.IW #5:
Wednesday, April 10th, 2013
We went over IW questions and then took the quiz.IW #4:
Monday, April 8th, 2013
We began by doing the practice problems at the ThatQuiz link above (be sure to have scratch paper!). Those who finished early worked on the shaded areas challenge on Khan Academy. We checked even answers on the IW and then continued our look at solids with more volume formulas. We watched this video on the volume of a pyramid, this video on the volume of a cone, this video of the surface area of a sphere, and this video on the volume of a sphere.IW #3:
Thursday, April 4th, 2013
We began by doing the area practice problems at the ThatQuiz link above (be sure to have scratch paper!). This led to a discussion of surface area and how to dissect a cylinder into its net. We then worked on these shaded area problems. We discussed the area formulas on p. 382 & 383, including Heron's area formula for triangles and the cool formula for the area of a triangle by its inscribed circle and perimeter... We then looked at our solids and some area and volume formulas.IW #2:
Tuesday, April 2nd, 2013
We began by correcting the Unit 6 test. We then investigated areas:- Log into Khan Academy and add obrienbluester@gmail.com as a coach.
- Watch the hints on the first parallelogram problem and then do the set of practice problems.
- Do this set of practice problems (using the hints if necessary).
In groups, we found the area of a regular hexagon with a side length of 6.2 cm. This led to a neat area formula with something called the apothem.IW #1:
Unit 6: Circles (standards and definitions/postulates/theorems)
Thursday, March 29th, 2013
Today was test day.IW #9:
Wednesday, March 27th, 2013
We began by going to the online Grade Calculator (make a copy for yourself (File- Make a copy...) and play with it). We then corrected the quiz and went over IW questions before taking a look at the final two sections of Chapter 6: locus and concurrence of lines. We reviewed the appropriate theorems and learned the mnemonic Many Cute People Believe Colorful Apples Bake In Airy Ovens. Questions on these two sections will be extra credit, but that's a great way to offset careless errors!!!IW #8:
Monday, March 25th, 2013
We began by going over any questions before the quiz. Those who finished early copied the seven Section 6-4 theorems into your Google Docs notebooks. After we reviewed the theorems, we worked on the assigned IW problems.IW #7:
Week of March 19th, 2013
Due to the snow day, Tuesday's work bumped to Thursday.Mr. O'Brien is out this week. Your sub Mr. Wheelis will help you out- he loves geometry! You may also email questions directly to Mr. O'B (link on left).
Tuesday
Begin by making sure that you've checked your Unit 6 quiz and reading notes sheet using the solutions posted with IW #5 below. Got questions on these or IW #5? Ask Mr. Wheelis...Spend the remainder of class working on the IW #6 sheets (answers posted below). Work from the back of the packet (9-7) to the front, as you might not have time to do all the problems in the hour dedicated to IW outside of class. Some problems involve the quadratic formula.
The questions on the quiz on Thursday will be taken directly from these four pages. You will not be able to use IW #6 during Thursday’s quiz (to avoid copying of answers without understanding).
IW #6:
Thursday, March 14th, 2013
We discussed IW questions on arc lengths, sectors, and circle segments.IW #5:
Tuesday, March 12th, 2013
We began class with the IW quiz. We then went over the most recent IW questions and learned about arc length, sectors, and circle segments.IW #4:
Friday, March 8th, 2013
We began class by taking a look at the Section 6.2 theorems involving secants and tangents. We used this applet to prove some of them. This led us to discuss the IW. We ended class with π, circumference, area, arc length, and sector area.IW #3:
Wednesday, March 6th, 2013
We began class by further investigating inscribed angles. Log into the Khan Academy and do this these three inscribed angle exercise sets: angle side on the diameter , angle sides enclosing the diameter , and angle sides outside the diameter. Before you do each problem set, watch the set of hints for each type; they prove that powerful Theorem 6.1.2. After our circle investigation, we corrected the Unit 5 test. We reviewed the section 6.1 theorems and went over the IW.IW #2:
Monday, March 4th, 2013
We began class by spending a little more time on the Unit 5 test. We then began our Unit 6 work by defining the following terms in our Google Docs notebook: circle, radius, chord, diameter, congruent circles, concentric circles, arc, semicircle, minor arc, major arc, central angle, inscribed angle, intercepted arc, measure of an arc, and congruent arcs. We then discussed a number of circle postulates and theorems and added them to our notebooks.IW #1:
Unit 5: Similar Triangles (standards and definitions/postulates/theorems)
ResourcesQuestions (assignment questions or general questions)
Even answers
ThatQuiz.org
Thursday, February 28th, 2013
Today was test day.IW #9:
Tuesday, February 26th, 2013
Mr. O'Brien was out today, so Ms. Nightingale went over the quiz and helped review for Thursday's test.IW #8:
Friday, February 15th, 2013
We began class by going over a special right triangle problem from the IW (if you are having trouble with special right triangles, this video might help!). We then investigated the neat theorem about how a triangle's angle bisector splits the side opposite it proportionally to the two sides that make it up. We proved the theorem and then took the quiz. We spent the remainder of class with this investigation:IW #7:
Wednesday, February 13th, 2013
We began class by doing some classwork practice: p. 249/26-29, 33, 38. We then corrected the quiz and spent some time discussing the two special right triangles and the IW. We finished by looking at dividing segments proportionally.IW #6:
Monday, February 11th, 2013
We began class with the quiz. Following that, we went over IW questions and learned about Pythagorean triples and the power of similarity for triangle problems. We finished by looking at our two special triangles: the 30-60-90, and the 45-45-90.IW #5:
Thursday, February 7th, 2013
We began class with notes on the geometric mean. We then constructed right triangles and their altitude inside the triangle. We printed them out and used them to discuss the geometric mean geometrically and several theorems leading to a proof of the Theorem of Pythagoras.IW #4:
Tuesday, February 5th, 2013
Unfortunately, Mr. O'Brien is home with a sick daughter this morning. Fortunately, you are in the capable hands of Ms. Nightingale! To begin, please open this sketch (in Firefox or Safari). Do the following:- Drag point A to get your own triangle.
- Write and solve two proportions in your notebook to find the lengths of a and of b.
- Check your answer by dragging down the blue and the green dots!
When you finish, please check the even answers to IW #3 (and #1 and #2 if you have not yet done so). Ms. Nightingale will go over the posted questions in class. Please make sure you have submitted the IW #1 and IW #2 sheets into the wire basket to be checked.Next, please open this sketch (in Firefox or Safari). Explore the three triangle similarity shortcuts and then copy Postulate 15 and Theorems 5.3.1 through 5.3.5 into your Google Docs and begin work on the practice sheet.
IW #3:
Friday, February 1st, 2013
We began class with a warm up to solve three quadratics. We used the Show Steps button in wolframalpha and the drop down menu of different solution methods. This led to a discussion of various ways to solve quadratics- simple square roots, factoring, and the quadratic formula. We then discussed the IW. This led to an introduction to similar polygons using this Geogebra applet.We finished by working on a classwork sheet.
IW #2:
Wednesday, January 30th, 2013
We began class by re-doing #18 from the test because of the typo. We then worked on correcting test errors in small groups. We took some notes on ratios, rates, and proportions, including three properties. We finished by working on a classwork sheet.IW #1:
Unit 4: Quadrilaterals (standards and definitions/postulates/theorems)
ResourcesQuestions (assignment questions or general questions)
Even answers
ThatQuiz.org
Thursday, January 24th, 2013
We began class with a self-correcting Always, Sometimes, Never quiz . The first three 100%'s earned extra credit! We then went over IW questions and made test revision questions in class for a class Jeopardy game. We finished with the game...IW #7:
Tuesday, January 22nd, 2013
We began class by going over the midterm. We then did p. 209-10/26 & 29 in pairs (and submitted) and then worked on finishing the Unit 4 Challenge problems p. 209/22, 25, 36.IW #6:
Monday, January 14th, 2013
We began class by correcting the quiz and discussing the midterm. We then went over IW #3 and worked on IW #4.IW #5:
Thursday, January 10th, 2013
We began class with the quiz. Following the quiz, we worked on part of IW#4. We then practiced with quadrilateral properties here. We finished by taking a look at the IW#3 questions. We learned about cyclic quadrilaterals and how to use the quadratic formula to find missing side lengths. We also talked a little about the midterm.IW #4:
Tuesday, January 8th, 2013
We began class by submitting the IW and finishing the quadrilateral jigsaw. Each group then presented their findings, beginning with a definition of their quadrilateral (from the glossary). We copied the remainder of the Unit 4 theorems into our Google Docs notebooks and went over the IW questions in preparation for the quiz next class.IW #3:
Thursday, January 4th, 2013
We began class by going over the answers to the Unit 3 test in preparation of the midterm. We then began a quadrilateral jigsaw .IW #2:
Wednesday, January 2nd, 2013
We began class by correcting the Unit 3 test. We noted that the definition of perpendicular lines does *not* include the words "right angle" or 90°; perpendicular lines are lines that form congruent adjacent angles. We then explored parallelograms and some interesting properties using paper and Geogebra. This sketch shows the relationships we found. We ended class by looking at p. 184/17 & 18.IW #1:
Archive
Unit 3: Triangles (standards and definitions/postulates/theorems)
ResourcesQuestions (assignment questions or general questions)
Even answers
ThatQuiz.org
Thursday, December 20th, 2012
Today was the test day.IW:
Tuesday, December 18th, 2012
We corrected the quiz and reviewed for Thursday's test with this Jeopardy game.IW #9:
Friday, December 14th, 2012
We began by going over Section 3-3 questions. After the quiz, we did two constructions and then discussed *why* some constructions work: copying an angle, bisecting an angle, and constructing a perpendicular from a point not on a line. We then reviewed the triangle inequality lemmas and theorems.IW #8:
Wednesday, December 12th, 2012
Unfortunately, Mr. O'B was out sick. From his sub plans:Students should begin by doing proofs #1, #3, and #10 on p. 171 in groups of three to submit to you. When they finish, please give them the triangle inequality sheets and ask them to read Section 3-5 and then complete the two sheets.
Their independent work is to complete the triangle inequality sheets and begin the Challenge problems. Please ask them to check that they did the correct IW #6- there was an error in iCal on Monday (although the website had the correct IW).
IW #7:
Monday, December 10th, 2012
We began class by correcting the quiz together and then we discussed the center of a triangle investigation.IW #6:
Thursday, December 6th, 2012
We began class by going over the IW and taking any questions before the quiz. We then took the quiz. Those who finished early, worked on the isosceles triangle practice sheet. When everyone was finished, we learned how to construct an angle bisector, a median, an altitude, and a perpendicular bisector for a triangle. We then worked on the Triangle Middle Exploration .IW #5:
Tuesday, December 4th, 2012
We began class with the Isosceles Triangle Construction challenge. This led to some familiarity with Geogebra and then some vocabulary and theorems about isosceles triangles. We went over an IW proof together and finished by defining angle bisector, median, altitude, and perpendicular bisector for a triangle.IW #4:
Friday, November 30th, 2012
We began class by going over the IW and some Unit 2 classwork. We then practiced with a congruent triangle problem set. We then looked at a special SSA case, the HL case, by looking at the triangle congruence applet. We then proved pp. 137/32 together and spent the remainder of our time working on congruence proofs from the IW. We finished class with by looking at CPCTC.IW #3:
Wednesday, November 28th, 2012
We began class by going over the Unit 2 tests. We discussed the connection between AAS and ASA and how they relate to AAA. We then used the the applet from last class to further explore the difference between SAS and SSA. We then proved pp. 137/32 together and spent the remainder of our time working on congruence proofs from the IW.IW #2:
Monday, November 26th, 2012
We began class by correcting the tests. We then explored triangle congruence tests using this applet: SSS, AAA, SSA, AAS, ASA, and SAS. Four became postulates/theorems, and two were discovered to be false...IW #1:
Unit 2: Parallel Lines (standards and rubrics and definitions/postulates/theorems)
November 15, 2012
We began class by going over IW questions. We then took the quiz. Those who finished early worked on the practice test. We finished class by going over the quiz.IW #8:
November 13, 2012
We began class with the quiz. Following the quiz, we read a little history of geometry on p. 118-119. We followed up by working on a group proof to submit: p. 91/29.IW #7:
November 8, 2012
Due to the snow delay, we postponed the quiz to next class. We discussed the IW #5 and the theorems and corollaries for polygons.IW #6:
November 6, 2012
We began class by going over IW and Quarter 1 assignments. We discussed grades and Challenge Problems. We then explored convex polygons: diagonals, interior angles, exterior angles.IW #5:
November 2, 2012
We began with a classwork assignment reviewing parallel and skew lines. We then took the quiz on Section 2.1. Mr. O'Brien gave some notes on triangles, including some vocabulary and a theorem with several corollaries. Mr. O'Brien then had to read the Riot Act on Challenge problems.IW #4:
Halloween, 2012
Mr. O'Brien is out today. After checking IW #2 (even answers posted above), the sub will give you a set of classwork practicing Sections 2.1 and 2.3. If you finish early, you may begin IW #3.IW #3:
Thursday, October 25th, 2012
We began class by playing with this Geogebra applet and answering the questions in our notebooks. We then discussed the postulates and theorems from Section 2.1. We also took a moment to look at the history of the Parallel Postulate. We went over the IW and then explored some converses leading to more theorems on proving lines parallel. This led to a discussion of inverse and contrapositive and the method of indirect proof, including the Law of Negative Inference.IW #2:
Tuesday, October 23rd, 2012
We began class by reading section 2.1 and taking reading notes. We also worked on adding definitions, theorems, and postulates to our Google Docs. We then worked on correcting Unit 1 errors in small groups.IW #1:
Unit 1: Line and Angle Relationships (standards and rubrics and definitions/postulates/theorems)
Monday, October 15th, 2012
We began class by going over the proof classwork that was due last week. We went over the IW and the rubrics for the Challenge problems and the unit standards. We spent the remainder of the period revising for the unit test.IW #15:
Thursday, October 11th, 2012
We warmed up with p. 57/21, 25, 27. We then went over the quiz and worked on revising for next week's unit test.IW #14:
Tuesday, October 9th, 2012
We began class with the quiz. We then went over the IW and the last theorems of Unit 1.IW #13:
Wednesday, October 3rd, 2012
We began class by learning our final construction of the unit: construct line perpendicular at a specific point on the given line. We then worked on classwork problems p. 50/1, 5-9, 26 to submit. We went over the evens and any questions from IW #11 and finished by discussing how to prove theorems.IW #12:
Monday, October 1st, 2012
We began with some angle and proof warm-up. We then corrected the IW and updated our Google Docs notebooks with Theorems 1.3.1 to 1.6.4 from p. A27 (proofs to come for some). We defined perpendicular lines, proved some theorems, and looked at relations and the Reflexive, Symmetric, Transitive properties for relations (i.e. congruence).IW #11:
Thursday, September 27th, 2012
We began by correcting the quiz from last class (solutions here) and discussing expectations in an honors course. We then began our work with geometric proof.IW #10:
Tuesday, September 25th, 2012
We began class with a quiz on section 1.1 to 1.3 and constructions. We then corrected the probability quizzes and the angle measuring worksheet and went over old IW questions.IW #9:
Friday, September 21st, 2012
We went over the probability quiz and reviewed angle vocabulary and problems.IW #8:
Wednesday, September 19th, 2012
We began class with the quiz and then warmed up with some angle measuring using the ThatQuiz link above. We also did a little worksheet which led us into angle measuring. We added two new postulates and several angle definitions to our notebooks (Keynote slide to copy-paste from available here).IW #7:
Monday, September 17th, 2012
We began class by reviewing probability. We then went over Challenge problem expectations and began our work developing geometry as a mathematical system, building up from postulates and definitions.IW #6:
Thursday, September 13th, 2012
We began class with the vocabulary quiz on Sections 1.1 and 1.2. We then went over IW #4, including the even answers (above). We finished our discussion on constructions (using both compass/straightedge and GeoGebra) and we then took notes on probability. Our objectives covered in class were 1.2, 1.3, and 1.9.IW #5:
Tuesday, September 11th, 2012
We began class by completing this introductory survey and reviewing the vocabulary of Section 1.2 with a worksheet. We discussed the Venn Diagram activity and IW #3. We learned how to make geometric constructions with a compass and straightedge and the corresponding GeoGebra tools. Our work covered objectives 1.1, 1.5, 1.9.IW #4:
Friday, September 7th, 2012
We began class by going over the IW (see even answers above). We reiterated the four elements of each IW (name, date, assignments, number) and discussed any questions, including the vocabulary words conjunction and disjunction. We reviewed the rubrics for objectives 1.1, 1.4, and 1.6 and then worked on the Venn Diagram activity. We finished with some notes on Section 1.2.IW #3:
Wednesday, September 5th, 2012
We began class with vanity plate introductions and discussed our use of rubrics this year. We then discussed independent work expectations, the responsibility points rubric and the independent work rubric (using this Prezi ). We began our Unit 1 work by reviewing the standards (rubrics here), the assessments, and the challenge problems. Those with laptops copied this Google Docs file and shared it with obrienbluester@gmail.com to start their class notebooks. We then took notes on sets, Venn Diagrams (using this Geogebra sketch ) and the Law of Detachment. The standards covered were 1.1, 1.4, and 1.6.IW #2:
Friday, August 31st, 2012
We began class with some introductions and a discussion of the course methodology, including expectations for class, the importance of independent work, how to get help, and more. We then used some intuition, inductive and deductive reasoning to answer some interesting questions and took a brief look at the standards for the unit and the challenge problems. We finishedby reviewing rubrics using vanity name plates.
IW #1: